A benchmark study on problems related to CO2 storage in geologic formations

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A benchmark study on problems related to CO2 storage in geologic formations
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  Comput Geosci (2009) 13:409–434DOI 10.1007/s10596-009-9146-x ORIGINAL PAPER A benchmark study on problems related to CO 2  storagein geologic formations Summary and discussion of the results Holger Class  ·  Anozie Ebigbo  ·  Rainer Helmig  ·  Helge K. Dahle  · Jan M. Nordbotten  ·  Michael A. Celia  ·  Pascal Audigane  ·  Melanie Darcis  · Jonathan Ennis-King  ·  Yaqing Fan  ·  Bernd Flemisch  ·  Sarah E. Gasda  · Min Jin  ·  Stefanie Krug  ·  Diane Labregere  ·  Ali Naderi Beni  ·  Rajesh J. Pawar  · Adil Sbai  ·  Sunil G. Thomas  ·  Laurent Trenty  ·  Lingli Wei Received: 12 August 2008 / Accepted: 15 June 2009 / Published online: 22 July 2009© Springer Science + Business Media B.V. 2009 Abstract  Thispapersummarisestheresultsofabench-mark study that compares a number of mathematicaland numerical models applied to specific problems inthe context of carbon dioxide (CO 2 ) storage in geo-logic formations. The processes modelled comprise ad- H. Class ( B ) · A. Ebigbo · R. Helmig · M. Darcis · B. FlemischUniversität Stuttgart, Stuttgart, Germanye-mail: holle@iws.uni-stuttgart.deA. Ebigboe-mail: ano@iws.uni-stuttgart.deR. Helmige-mail: rainer@iws.uni-stuttgart.deM. Darcise-mail: melanie.darcis@iws.uni-stuttgart.deB. Flemische-mail: bernd.flemisch@iws.uni-stuttgart.deH. K. Dahle · J. M. NordbottenDept. of Mathematics, University of Bergen,Bergen, NorwayH. K. Dahlee-mail: Helge.Dahle@math.uib.noJ. M. Nordbottene-mail: Jan.Nordbotten@math.uib.noJ. M. Nordbotten · M. A. CeliaDept. of Civil and Environmental Engineering,Princeton University, Princeton, NJ, USAe-mail: celia@princeton.edu vective multi-phase flow, compositional effects due todissolution of CO 2  into the ambient brine and non-isothermaleffectsduetotemperaturegradientsandtheJoule–Thompson effect. The problems deal with leak-age through a leaky well, methane recovery enhanced P. AudiganeBRGM, French Geological Survey, Paris, Francee-mail: p.audigane@brgm.frJ. Ennis-KingCooperative Research Centre for GreenhouseGas Technologies, CSIRO Petroleum,Kensington, Australiae-mail: Jonathan.Ennis-King@csiro.auY. FanDept. of Energy Resources Engineering,Stanford University, Stanford, CA, USAe-mail: yaqingf@gmail.comS. E. GasdaUniversity of North Carolina at Chapel Hill,Chapel Hill, NC, USAe-mail: sgasda@unc.eduM. JinHeriot-Watt University, Edinburgh, UKe-mail: Min.Jin@pet.hw.ac.ukS. KrugBundesanstalt für Geowissenschaftenund Rohstoffe (BGR),Hannover, Germanye-mail: stefanie.krug@bgr.de  410 Comput Geosci (2009) 13:409–434 by CO 2  injection and a reservoir-scale injection sce-nario into a heterogeneous formation. We give adescription of the benchmark problems then brieflyintroduce the participating codes and finally presentand discuss the results of the benchmark study. Keywords  Benchmark  ·  Code comparison  · CO 2  storage 1 Introduction Mathematical models and numerical simulators areessential tools in addressing problems and questionsthat arise in the context of CO 2  storage in the deepsubsurface. They are necessary for the clarification of safety, feasibility and economic issues. The elaborationofalegalframeworkthatallowsforalarge-scaleimple-mentation of the carbon capture and storage (CCS)technology will probably also require such models.In order to transfer laboratory results to the scale of application of the CCS technology, it is necessary tounderstand the relevant physical processes and to im-plement them in mathematical and numerical models.Numerical models are useful for CCS projects in thepreparationandapprovalstage,duringinjectionopera-tions and after injection has ended. Models shouldaccompanythelifecycleofaproject.Numericalmodelsare also used to aid in decision making.Therefore, it is a crucial task to build confidence inthe results and outputs of numerical simulators andmathematical models. It is important to understandhow sensitive different model concepts and numericalapproaches are with respect to given questions. Sinceit is not possible to validate models for CO 2  storagecomprehensively by means of well-controlled measure-ments,apragmaticapproachcouldbetoinvestigatethe D. LabregereSchlumberger Carbon Services,Paris, Francee-mail: dlabregere@slb.comA. Naderi BeniE.ON Energy Research Centre, Institute of Applied Geophysics and Geothermal Energy,RWTH Aachen University,Aachen, Germanye-mail: anaderi@eonerc.rwth-aachen.deR. J. PawarLos Alamos National Laboratory, Los Alamos,NM, USAe-mail: rajesh@lanl.gov range of model predictions for a number of benchmarkproblemswhereprecisedescriptionsofmodeldomains,boundary conditions, etc., are given.This benchmark study for mathematical models andnumerical simulators focuses on injection scenarios indeep geologic formations. In general, the physical sys-tems can be described by multi-phase multi-componentconcepts including non-isothermal effects which occurmainly near the injector due to pressure-lowering andexpansion of the CO 2  (Joule–Thompson effect). Arapid gas expansion correlated with Joule–Thompsoncooling can also occur in highly permeable verticalpathways such as leaky wells. The CO 2  experiences acontinuous reduction in pressure as it rises. In recentyears, there have been different numerical and analyti-cal concepts developed for the simulation of such prob-lems.Still,thevalidationofthesemodelsischallenging,since the necessary data on the relevant scales are notsufficiently available. For assessing the reliability andaccuracy ofthe differentconcepts, we consideritessen-tial to formulate benchmark problems that can be usedfor model intercomparisons. This study can be viewedas a follow-up of recent benchmark studies like theGEO-SEQ Code Intercomparison Study [50] initiatedat Lawrence Berkeley National Laboratory. The newbenchmarks focus on 3D geometries and consider thesophistication and improvement of the model conceptsthat have been achieved since then. A first presenta-tion of the benchmarks and the preliminary results of the intercomparison study was given at the  Workshopon Numerical Models for CO 2  Storage in Geological Formations  that took place from 2–4 April, 2008, inStuttgart, Germany [1].The topics addressed in this study are– Leakage of injected CO 2  into overlying formationsthrough a leaky well (problem 1) A. SbaiBRGM, French Geological Survey, Orleans, Francee-mail: a.sbai@brgm.frS. G. ThomasTexas University, Austin, TX, USAe-mail: sgthomas@ices.utexas.eduL. TrentyTechnology, Computer Science and Applied MathematicsDivision, IFP, Rueil-Malmaison Cedex, Francee-mail: laurent.trenty@ifp.frL. WeiShell International Exploration and Production BV,Rijswijk, The Netherlandse-mail: Lingli.Wei@Shell.com  Comput Geosci (2009) 13:409–434 411 – Enhanced gas recovery (EGR) by injection of CO 2 (problem 2)– CO 2  plume spreading and dissolution and storagemechanisms in a large-scale heterogeneous reser-voir (problem 3)The dominant physical processes and the trappingmechanismsduringandaftertheinjectionofCO 2  intoageologicalformationvarysignificantlyovertime.Thisisschematically illustrated in Fig. 1. During injection and in the first phase after injection, advective multi-phaseprocesses dominate the CO 2  spreading. This is drivenby viscous forces due to the injection overpressure andby buoyancy due to the density differences. After sometime, multi-phase flow slows down and the effect of dissolution of CO 2  into the brine increases. The timescales considered in this study are up 50 years, which is,in general, not sufficient to dissolve the injected CO 2 completely or generate significant mineralisation dueto geochemical reactions. Geochemical mineralisationprocesses like precipitation of calcite are not consid-eredatthecurrentstageofthisbenchmarkstudy.Othershort-term chemical reactions, like the production of carbonicacidfromwaterandCO 2  orbiological/organiceffects in the near well bore region, are also excluded.This paper gives the definition of the three bench-mark problems, including one variation for eachproblem (Section 2). Thereafter, an overview of theparticipating groups and their applied models is given 2 time after stop of CO - injection (years)10,0001,000100101 structural and stratigraphictrappingresidualtrappingsolubilitytrappingmineraltrapping    t  r  a  p  p   i  n  g  c  o  n   t  r   i   b  u   t   i  o  n   % 1000(viscous, buoyant, capillary)behavioradvection- dominatedphase transfer processesgeochemicalreactionsmultiphasedissolution and diffusion    d  o  m   i  n  a   t   i  n  g  p  r  o  c  e  s  s  e  s increasing storage security Fig. 1  Variation of the trapping mechanisms and the dominantprocesses on different time scales (modified after [28]) (Section 3), as well as a summary of the results of thedifferent problems (Section 4). An attempt is made torecapitulate the lessons learned so far from the bench-mark study including the process of formulating bench-marks and evaluating results (Section 4.4). Finally,Section 5 gives some closing remarks. 2 Definition of the benchmark problems This section gives the definitions of the three bench-mark problems. For each problem, a brief problem-oriented motivation is given. The model domains,model input parameters, boundary conditions, simu-lation times and expected model outputs for the in-tercomparison are specified. The people involved inthe formulation of the benchmarks are listed for eachproblem.2.1 Definition of benchmark problem 1: CO 2  plumeevolution and leakage through an abandoned well  2.1.1 Formulated by A. Ebigbo, J. Nordbottenand H. Class This benchmark problem is developed using [40–42] as references.Adescriptionanddiscussionoftheproblemhave been published in [20]. It addresses the simulation of the advective spreading of CO 2  injected into anaquifer,whichisobviouslyanimportantprocesssinceitdetermines the distribution of CO 2  in the aquifer overtime. A second topic addressed by the problem set-up is the leakage of CO 2  from the aquifer through anabandoned and leaky well. Problem description  CO 2  is injected into an aquifer;spreads within the aquifer and, upon reaching a leakywell, rises up to a shallower aquifer. A quantification of the leakage rate which depends on the pressure build-up in the aquifer due to injection and on the plumeevolution is the goal of the simulation.This scenario is shown in Fig. 2. The simulation domain has a lateral extent of   1 , 000 × 1 , 000  m. At thelateral boundaries, constant boundary conditions areimposed on the system. The leaky well is at the centreof the domain and the injection well is 100 m away.Both aquifers are 30-m thick and the aquitard has athickness of 100 m. The leaky well is modelled as aporous medium with a higher permeability than theformation.Two cases (problem 1.1 and problem 1.2) are of interest. In problem 1.1, the aquifer is very deep and a  412 Comput Geosci (2009) 13:409–434 30 m100 m30 mCO2 plumeleaky wellinjection well100 maquiferaquiferaquitard Fig. 2  Leakage scenario number of simplifying assumptions are made. In prob-lem 1.2, the aquifer is much shallower and the CO 2 can change state while rising to the top aquifer. Theproblem is also much less restricted by simplificationsthan problem 1.1. Table 1 lists the properties of thedomain, Table 2 the fluid properties for both cases, andTable 3 the hydraulic properties of the porous media.In problem 1.2, modellers are expected to describethe CO 2  and brine fluid properties as functions of theaquifer conditions. As the CO 2  rises, it experienceslarge changes in fluid properties. These changes areexpected to have a strong influence on the CO 2  leakagerate. The density, specific heat capacity and thermalconductivity of the solid phase (porous medium) arealso given for problem 1.2 as  ρ  s  =  2,650 kg/m 3 ,  c  s  = 750  J/(kg K) and  λ  s  = 3 . 5  W/(m K), respectively. Table 1  Domain geometryParameter ValueProblem 1.1 Problem 1.2Aquifer depth 2,840–3,000 m 640–800 mAquifer thickness 30 mAquitard thickness 100 mDimensions of the model domain 1,000 m × 1,000 m × 160 mDistance between wells 100 mLeaky & injection well radius 0.15 m  Initial and boundary conditions  The initial conditionsin the domain include a hydrostatic pressure distribu-tion, which is dependent on the brine density, and ageothermal temperature distribution (for problem 1.2)dependentonthegeothermalgradient.Thegeothermalgradient is 0.03 K/m and the initial temperature atthe bottom (at 800 m depth) is 34  ◦ C. The aquifersare initially filled with brine. The initial pressure atthe bottom of the domain is  3 . 086 × 10 7 Pa for prob-lem 1.1 (at 3,000 m depth) and  8 . 499 × 10 6 Pa forproblem 1.2 (at 800 m depth). The lateral boundary Table 2  Fluid properties are constant in problem 1.1Parameter ValueProblem 1.1 Problem 1.2CO 2  density 479 kg/m 3  f  ( T  ,  p ) Brine density 1,045 kg/m 3  f   T  ,  p , S ,  X  CO 2 w  CO 2  viscosity 3.950 × 10 − 5 Pa · s  f  ( T  ,  p ) Brine viscosity 2.535 × 10 − 4 Pa · s  f  ( T  , S ) CO 2  enthalpy isothermal  f  ( T  ,  p ) Brine enthalpy isothermal  f   T  ,  p , S ,  X  CO 2 w  Mutual solubilities neglected  f  ( T  ,  p , S ) Inproblem1.2,theyaredependentontemperature T  ,pressure  p ,brine salinity  S = 0 . 1  kg NaCl per kilogram solution (brine) andCO 2  mass fraction in brine  X  CO 2 w  . Hence, no values are given inthe table. The description of the fluid properties in problem 1.2 iscompletely up to the individual modellers. This aims at showingtherangeofimplementationsandassumptionsforthecalculationof the fluid properties by the different models  Comput Geosci (2009) 13:409–434 413 Table 3  Porous media properties (homogenous) and porousmedium-fluid parametersParameter ValueProblem 1.1 Problem 1.2Aquifer permeability  2 × 10 − 14 m 2 Leaky well permeability  1 × 10 − 12 m 2 Porosity 0.15Residual brine saturation 0 0.2Residual CO 2  saturation 0 0.05Relative permeability linear ( k r  α  =  S α ) [10]Capillary pressure,  −  [10]  p c  ≤ 5 × 10 5 PaEntry pressure  −  10 4 PaBrooks-Corey parameter  λ  −  2.0 conditions are constant Dirichlet conditions and equalto the initial conditions. All other boundaries are no-flow boundaries.CO 2  is injected at a constant rate of 8.87 kg/s.In problem 1.1, this corresponds to 1,600 m 3 /day.It is assumed (for problem 1.2) that the CO 2  is in- jected at a constant temperature of 33.6  ◦ C. Simulationtime is 1,000 days for problem 1.1 and 2,000 days forproblem 1.2. Output   The output of interest is the CO 2  leakagethrough the leaky well as a function of time. This isdefined here as the CO 2  mass flow at midway be-tween top and bottom aquifers divided by the injectionrate, in percent. The maximum leakage value and theleakage value at  t  =  1,000 days (for problem 1.1) and t  = 2,000 days (for problem 1.2) are to be given.In problem1.2,the effectofleakingCO 2  onthetem-perature in the vicinity of the leakage is to be shown bygiving the temperature in the leaky well at the bottomof the top aquifer (at a depth of 670 m) over time.2.2 Definition of benchmark problem 2: enhancedCH 4  recovery in combination with CO 2  storagein depleted gas reservoirs  2.2.1 Formulated by A. Ebigbo and H. Class Depleted gas reservoirs are potential target forma-tions for CO 2  sequestration purposes [45, 65]. Such reservoirs have stored gases for very long periods of time and are therefore well suited for CO 2  storage.Injected CO 2  would displace the native gas (in thiscase, methane, CH 4 ), increasing its production fromthe reservoir. Infrastructure such as well and pipelinesoften already exists in gas fields and reduces the costof CO 2  storage. However, during gas production, thereservoir experiences large changes in pressure whichmay compromise the sealing capability of the cap rock. injection wellmodelled areaproduction well Fig. 3  Five-spot pattern depicting the CO 2  injection well and theCH 4  production wells Theproblemdescribedheredealswiththestorageof CO 2  in such a depleted reservoir. Interesting processesinclude the mixing of the gases, the changes in physicalproperties of the gas mixture with composition and theamount of CH 4  which can be recovered before CO 2 breakthrough. Problem description  Numerical modelling of CO 2  in- jection into a gas reservoir in a five-spot pattern hasbeen done by [44] and [58]. This is a good representa- tion of a generic enhanced gas scenario and will bethe basis of this benchmark problem. Figure 3 showsa schematic of the five-spot problem with an injectionwell at the centre and production wells at the corners.Due to symmetry, only a quarter of the domain ismodelled.The properties of the reservoir are identical to thosesuggestedin[58]andaregiveninTable4.Sincenumer- ical diffusion has a strong influence on the mixing of  Table 4  Reservoir properties (from [58]) and simulationparametersProperty ValueQuarter five-spot area 40,477 m 2 (201.19 m × 201.19 m)Reservoir thickness 45.72 mPorosity 0.23Brine saturation 0Reservoir temperature (isothermal) 66.7  ◦ CDepleted reservoir (initial) pressure 35.5 barCoefficient of molecular diffusion  6 × 10 − 7 m 2 /sProblem 2.1Horizontal permeability  50 × 10 − 15 m 2 Vertical permeability  5 × 10 − 15 m 2
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